Peemoeller and Stevens: Age, size, and sexual maturity of Busycotypus canaiicuiatus in Buzzards Bay, Massachusetts 
269 
cinum isaotakii (e.g., llano et al., 2003) and Rapana 
venosa (e.g., Mann et al., 2006). Male gonads exhibit- 
ed 4 stages: immature (I), early developing (ED), late 
developing (LD), and mature (M). Male maturity was 
classified on the basis of the presence of spermatozoa 
in the tubule and not on the basis of density. For classi- 
fication in a fifth stage, the recovering (R) stage, males 
would be expected to exhibit elongate tubules with few 
remaining spermatozoa. No males were considered in 
the R stage because all males with elongate tubules 
had >50% of tubules with spermatozoa and were sub- 
sequently reported as in the mature stage. Female go- 
nads exhibited 5 stages: I, ED, LD, M, and R. Female 
maturity was determined on the basis of the amount of 
vitellogenic oocytes (VOs) present in the cross section. 
Statistical analyses 
Linear regression relationships between SL, LW, and 
Wt were calculated and compared through the use of 
covariance analysis to determine if there was a rela- 
tionship between sex and shell size or shape (Stoner et 
al., 2012). A significant coefficient CP<0.05) meant that 
either slope or intercept differed between males and 
females. As a prerequisite for covariance analysis, an 
F-test was used to ensure that the variance between 
males and females was not significantly different. Data 
were logio transformed for the relationship between SL 
and Wt because Wt increased nonlinearly to SL. For 
the comparison of logio SL and sex to logio Wt, sex was 
a factor and logjo SL was a covariate. 
The von Bertalanffy growth model has been used to 
describe the growth of gastropods, such as the queen 
conch ( Strombus gigas) (e.g., Berg and Olsen, 1989) 
and Buccinum isaotakii (e.g., llano et al, 2004). Shell 
length and estimated age for each channeled whelk 
were used to fit a von Bertalanffy growth model, for 
each sex separately (Ricker, 1975): 
L a - Li n f (1 - e K(a V), 
where 
^inf — 
K = 
a = 
to = 
the SL (in millimeters) at age (years); 
the theoretical maximum SL; 
the growth coefficient; 
the age; and 
the theoretical age at length 0. 
A von Bertalanffy growth model that compared LW (in 
millimeters) and estimated age also was conducted, 
with LW replacing SL where appropriate. The annual 
growth rate (in SL) for each sex was calculated by sub- 
tracting the size at each age from the size at age+1 
from the von Bertalanffy growth model. Growth rate 
and age were square-root (sqrt) transformed and co- 
variance analysis was used to determine if sex affects 
growth. The sqrt transformation was used because a 
log 10 transformation yielded nonlinear results. The re- 
gression of sqrt-transformed SL growth versus age and 
sex included sex as a factor and sqrt (age) as a covari- 
ate and was expressed (in terminology of R statisti- 
cal software [R Development Core Team, 2011]) in this 
manner: 
sqrt (SL growth) ~ sqrt (age) * sex, 
where ~ indicates a relationship (“modeled as”) and * 
indicates the combination of the factors sqrt (age) + 
sex and the interaction of sqrt (age) by sex. All further 
regression equations used this terminology and were 
computed with R statistical software (R Development 
Core Team, 2011). 
On the basis of results of reproductive histology, we 
classified as mature any whelk with gonads in stage 
M or R. These data were used to calculate a nonlin- 
ear logistic regression by using a general linear model 
(GLM) with a binomial link function, with SL, LW, or 
age as the size measurement, and the GLM regression 
coefficients were used to estimate the size at which 
channeled whelk of each sex reached SM50 with the 
following formula: 
SM 50 = 
where Bq = the intercept; and 
B\ = the slope. 
Because the SM50 equation gives only a single value 
for each data set (male or female), a bootstrap routine 
was used to resample each data set with replacement 
1000 times, and the results were used to calculate the 
bias and standard error (SE) of the original mean value 
of SM50. Bias was calculated through the subtraction of 
the original (full data set) value of SM50 from the resa- 
mpled mean value of SM50. SM50 is a widely accepted 
predictor of sexual maturity for various shellfishes, 
including the queen conch (e.g., Stoner et al., 2012), 
waved whelk (e.g., Heude-Bertherlin et al., 2011), and 
Zidona dufresnei (e.g., Gimenez and Penchaszadeh, 
2003). In our study, the fitted values of the GLM, rep- 
resenting the proportion of mature whelk, were plotted 
against either SL or LW. For comparison, the propor- 
tion of mature whelk was calculated from the raw data 
within 10-mm increments of SL or 5-mm increments of 
LW and plotted. To compare the LW at which each sex 
reached SM50 with the current minimum size limit for 
harvest, we conducted a regression that compared the 
LW of 166 channeled whelk to their SW, the measure- 
ment similar to the one used to specify the legal size 
limit. All SM50 values are given as mean ±1 SE, and all 
statistics were computed with R (R Development Core 
Team, 2011). 
Results 
Staging gonads 
Seawater temperatures at Woods Hole in the sampling 
months of August 2010 and July 2011 averaged 22.2°C 
(SE 0.7) and 22.2°C (SE 0.6), respectively, and were 
not significantly different, but mean temperatures in 
August were 1.2°C greater in 2011 than in 2010. To our 
